Convergence of the Abelian sandpile

The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice $\mathbb{Z}^d$, in which sites with at least 2d chips {\em topple}, distributing 1 chip to each of their neighbors in the lattice, until no more topplings are possible. From an initial configuration consisting of $n$ chips placed at a single vertex, the rescaled stable configuration seems to converge to a particular fractal pattern as $n\to \infty$. However, little has been proved about the appearance of the stable configurations. We use PDE techniques to prove that the rescaled stable configurations do indeed converge to a unique limit as $n \to \infty$. We characterize the limit as the Laplacian of the solution to an elliptic obstacle problem.Comment: 12 pages, 2 figures, acroread recommended for figure displa

Matching and Independence Complexes Related to Small Grids

The topology of the matching complex for the $2\times n$ grid graph is mysterious. We describe a discrete Morse matching for a family of independence complexes $\mathrm{Ind}(\Delta_n^m)$ that include these matching complexes. Using this matching, we determine the dimensions of the chain spaces for the resulting Morse complexes and derive bounds on the location of non-trivial homology groups for certain $\mathrm{Ind}(\Delta_n^m)$. Further, we determine the Euler characteristic of $\mathrm{Ind}(\Delta_n^m)$ and prove that several homology groups of $\mathrm{Ind}(\Delta_n^m)$ are non-zero

Apollonian structure in the Abelian sandpile

The Abelian sandpile process evolves configurations of chips on the integer lattice by toppling any vertex with at least 4 chips, distributing one of its chips to each of its 4 neighbors. When begun from a large stack of chips, the terminal state of the sandpile has a curious fractal structure which has remained unexplained. Using a characterization of the quadratic growths attainable by integer-superharmonic functions, we prove that the sandpile PDE recently shown to characterize the scaling limit of the sandpile admits certain fractal solutions, giving a precise mathematical perspective on the fractal nature of the sandpile.Comment: 27 Pages, 7 Figure

Revenue Insurance and Chemical Input Use Rates

Using farm level data and a simultaneous probit model we evaluate the input use and environmental effects of revenue insurance. A priori, the moral hazard effect on input use is indeterminate and this study empirically assesses the input use impact of the increasingly popular, and federally subsidized, risk management instrument of revenue insurance. We conclude that the moral hazard effect of federally subsidized revenue insurance products induces U.S. wheat farmers to increase expenditures on pesticides and reduce expenditures on fertilizers.Crop Production/Industries, Risk and Uncertainty,

Strategic Leadership in the 21st Century

In honor of the 60th Anniversary of the founding of Israel The Carl and Dorothy Bennett Center for Judaic Studies presents General Wesley K. Clark (ret.), \u27Strategic Leadership in the 21st Century.\u27https://digitalcommons.fairfield.edu/bennettcenter-posters/1259/thumbnail.jp

Estimating a range of flow rates resulting from extreme storm events within the Wekiva River watershed through statistical testing and modeling

The middle portion of the St. Johns River is located in East-Central Florida, USA. This region of the St. Johns River is increasingly subject to urbanization and conversion of forest areas to agricultural land. Overall, these changes mean that future flood events in the area could adversely impact local citizens. Therefore, the examination of extreme flood events and resiliency to such events is critical. The purpose of this preliminary study is to explore a range of practical applications to estimate extreme flood flows at watercourses within the Middle St. Johns River Basin, focusing specifically upon the Wekiva River sub-basin. The current work illustrates the overall technical methodology and provides estimates of extreme flood flows at different return frequencies using hydrologic modeling, statistical analysis, and supporting published reports. Altogether, once fully integrated and complete, the methods will permit predictions at a range of possible flood flows as a result of an extreme storm event at any place along the watercourse